The lowest valence transitions of 1,1′-bicyclohexylidene and 1,1′;4′,1′-tercyclohexylidene. An ab initio MRDCI study1

Chemical Physics 225 Ž1997. 139–152

The lowest valence transitions of 1,1X-bicyclohexylidene and 1,1X ;4X ,1X-tercyclohexylidene. An ab initio MRDCI study 1 Remco W.A. Havenith a

a,b

, Joop H. van Lenthe b,) , Leonardus W. Jenneskens a , Frans J. Hoogesteger a

Debye Institute, Department of Physical Organic Chemistry, Utrecht UniÕersity, Padualaan 8, 3584 CH Utrecht, The Netherlands b Debye Institute, Theoretical Chemistry Group, Utrecht UniÕersity, Padualaan 8, 3584 CH Utrecht, The Netherlands Received 4 April 1997

Abstract Ab initio MRDCI calculations were performed on the oligoŽcyclohexylidenes. 1,1X-bicyclohexylidene Ž1. and 1,1X :4X ,1Ytercyclohexylidene Ž2. using RHFr6-31G geometries and molecular orbitals for the assignment of their lowest valence transitions taking into account the four lowest states of each symmetry. The calculations unequivocally show that the valence transitions of 1 and 2 correspond to p ™ p ) and p ™ s ) transitions. In the case of 1, the MRDCI results were verified by Direct-CI calculations. Mulliken population analyses suggest that the p ™ s ) transitions possess charge transfer character; upon excitation electron density shifts from the olefinic carbon atoms towards hydrogen atoms positioned in the cyclohexylidene rings. The transition energies and oscillator strengths of the p ™ p ) and p ™ s ) transitions of 1 and 2 differ from those of the reference compounds tetramethylethene Ž3. and 1,4-diisopropylidene-cyclohexane Ž4., respectively. In going from 3 to 1 both the p ™ p ) and the first s ™ p ) transitions of 1 are bathochromically shifted by ca. 0.24 eV. The first p ™ s ) transition of 1 is hypsochromically shifted Ž0.79 eV. with respect to that of 3. In the case of 2 both the p ™ p ) and p ™ s ) transitions are ca. 0.9 eV bathochromically shifted with respect to those of 4. q 1997 Elsevier Science B.V.

1. Introduction OligoŽcyclohexylidenes. composed of cyclohexyl rings connected via carbon–carbon double bonds, which contain functionalities at the a- and v-positions, were recently proposed as novel molecular building blocks for supramolecular and functional systems w1–3x. Derivatives bearing an oxime functionality at an end position were shown to be suitable )

Corresponding author. Fax: 030 253 7504 Dedicated to Prof. Dr. S.D. Peyerimhoff on the occasion of her sixtieth birthday. 1

amphiphiles for Langmuir film formation at the airrwater interface, which could be transferred onto hydrophilic silicon substrates w1x. Furthermore, derivatives containing at the a , v-positions an electron donor and electron acceptor moiety, respectively ŽwDsAx., were shown to possess opto-electric properties. Upon excitation of wDsAx to either a local wD ) sAx or wDsA) x state, rapid intramolecular electron transfer occurs leading to the population of a dipolar, charge separated state wDqPsAyPx ) w3x. Hence, the intervening oligoŽcyclohexylidene. bridge can be envisaged as a semi-rigid redox-active moiety. To deepen our insight in the factors contributing

0301-0104r97r$17.00 q 1997 Elsevier Science B.V. All rights reserved. PII S 0 3 0 1 - 0 1 0 4 Ž 9 7 . 0 0 1 7 4 - 2

140

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

to the photoinduced charge separation w4x process we were prompted to study the photophysical properties of the oligoŽcyclohexylidenes.. It is noteworthy that the simplest representative of the oligoŽcyclohexylidene. series, viz. 1,1X-bicyclohexylidene Ž1., has already received considerable attention due to its peculiar UV spectrum both in the solid-state and solution in comparison with that of a related reference compound, viz. tetramethylethene Ž3.. Both in the vapor phase and in solution Žsolvent: n-pentane. the UV absorption spectrum of 1,1X-bicyclohexylidene Ž1. contains two distinct bands centered at 5.95 eV and 6.82 eV, and, at 6.01 eV and 6.85 eV, respectively w5,6x, whereas for 3 only one band at 7.0 eV attributed to a p ™ p ) valence transition was found w7x. Unequivocal evidence that the two UV absorption bands of 1 are due to valence transitions was obtained from the solid-state UV spectrum of a single crystal of 1; two bands at 5.95 eV and 6.32 eV were found which both were shown to be polarized along the carbon–carbon double bond CŽ1. –CŽ2. w8x. Similar results were found for a solid-solution of 1 in stretched polyethylene films w9x. Since Rydberg transitions possess vanishingly low intensities both in the solid-state and in solution, they have to be attributed to valence transitions. The 5.95 eV Ž6.01 eV. band of 1 was assigned to a p ™ p ) valence transition. However, the assignment of the 6.82 eV Ž6.85 eV. band was less straightforward. It was tentatively concluded to correspond with a charge transfer X p ŽCH 2 .X ™ p ) valence transition in which electron density is shifted from the cyclohexyl rings into the carbon–carbon double bond w5,10,11x. To explain the difference in absorption spectra of 1 and 3 and to obtain a reliable assignment of their valence transitions ab initio MRDCI calculations using RHFr6-31G geometries and molecular orbitals ŽMO’s. taking into account the two lowest excited states of each symmetry were recently performed by some of the present authors w12x. The 6-31G basis set, which does not contain polarization functions, was used to circumvent the inclusion of Rydberg character into the transitions. The results showed that the first valence transition of 1 is indeed a p ™ p ) transition. However, in contrast with the previous proposal w5x, the second transition had to be unequivocally assigned to a p ™ s ) transition. In line with

the solid-state w8x and solid solution w9x UV data both transitions were polarized along the carbon–carbon double bond CŽ1. –CŽ2.. Moreover, Mulliken population analysis w13x revealed that the p ™ s ) transition possesses charge transfer character, viz. electron density is shifted from the carbon–carbon double bond towards the equatorial hydrogen atoms of the cyclohexylring moieties. The objective of this paper is three-fold: Ž1. In our initial ab initio MRDCI w14,15x study two states per symmetry of 1 were calculated using ca. 5000 configuration state functions ŽCSF’s. per symmetry for the assignment of the lowest valence transitions. To probe the convergence of the MRDCI results, the calculations were repeated taking into account ca. 60000 CSF’s and four states per symmetry. The latter extension is a prerequisite for the calculation of the lowest valence transitions of the next higher homologue of 1, viz. 1,1X :4X ,1Y-tercyclohexylidene Ž2.. For 2 it is anticipated that through-bond interactions w16x between the carbon–carbon double bonds will be operational. Hence, MRDCI calculations using only two states per symmetry will not be sufficient to give estimates of the p ™ s ) transitions. Ž2. Furthermore, the reliability of the ab initio MRDCI approach, viz. the influence of the frozen core approximation and the configuration selection procedure for 1 was evaluated by doing Direct-CI w17x calculations on the ground state Ž1A g . and several excited states Ž1B u , 2B u and 1B g .. 3. Since the results reveal that the MRDCI approximations are appropriate, the lowest valence transitions of 1,1X :4X ,1Y-tercyclohexylidene Ž2. were calculated taking into account four states per symmetry. To assist the interpretation of the MRDCI results obtained for 2 the reference compound 1,4-diisopropylidenecyclohexane Ž4. was also studied. 2. Computational details All calculations were run on a Silicon Graphics Power Challenge computer using the quantum chemical program system GAMESS-UK w18x and its MRDCI package w19x. All geometries were optimized at the RHFr6-31G level Ž1, 2, 4 and 5; C 2h symmetry and 3; D 2 symmetry. and were characterized as local minima by means of a Hessian calculation.

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

MRDCI w14,15x calculations were performed using the RHFr6-31G geometry and molecular orbitals ŽMO’s.; transition energies and oscillator strengths Ž f . were calculated for the four lowest states of each symmetry. The active CI space of 1 and 2 consisted of 10 occupied MO’s Ž20 electrons. and 88 virtual MO’s. Configuration selection w20x for 1 resulted in the inclusion of 56740 CSF’s of A g , 62452 CSF’s of A u , 69783 CSF’s of B u and 66311 CSF’s of B g symmetry. In the case of 2, 62154 CSF’s of A g , 63549 CSF’s of A u , 49207 CSF’s of B u , and of 43734 CSF’s of B g symmetry were included. The active CI space of 3 consisted of 13 occupied MO’s Ž26 electrons. and 54 virtual MOs. The configuration selection procedure gave 83295 CSF’s of A 1 , 88043 CSF’s of B 1 , 88427 CSF’s of B 2 , and 86363 CSF’s of B 3 symmetry. The active CI space of 4 consisted of 15 occupied MO’s Ž30 electrons. and 68 virtual MO’s furnishing 84986 CSF’s of A g , 63521 CSF’s of A u , 67089 CSF’s of B u , and 66907 CSF’s of B g symmetry. Direct-CI w17x calculations were performed for 1 on the 1A g ground state, and the 1B u , 2B u and 1B g excited states with the ATMOL w21x program package to test the influence of the frozen core and the configuration selection procedure in the MRDCI calculations. In the Direct-CI calculations only the twelve 1s orbitals on carbon of 1 were frozen. Both MRDCI and Direct-CI energies were corrected for size-consistency errors by the Davidson correction w22x ,generalized for multi-reference CI expansions. This is done in the MRDCI calculations by taking for c 20 , the sum of the squares of the coefficients of all the reference configurations w15x, while in the Direct-CI calculations c 0 is a projection of the reference function on the CI function w23x. Ground state and excited state electron distributions were calculated by Mulliken population analyses w13x.

141

X

Fig. 1. RHFr6-31G geometry of 1,1 -bicyclohexylidene Ž1.

Žbond lengths, valence angles and dihedral angles. are in satisfactory agreement with those found by single crystal X-ray analysis w24x. It is noteworthy that in the solid-state 1 only possesses ‘‘approximate’’ C 2h symmetry. Besides a crystallographic inversion center, a non-crystallographic mirror-plane perpendicular to the carbon–carbon double bond CŽ1. –CŽ2. bisecting the carbon atoms CŽ11. and CŽ12. is found. The RHFr6-31-G geometries of 2 and its reference compounds 4 as well as 1,4-dimethylidenecyclohexane Ž5. are shown in Figs. 2 and 3, respectively. Unfortunately, no single crystal X-ray structure is available for 2. However, a comparison of its RHFr6-31G structure with the single crystal X-ray structure of an 1X ,1X-bis-alkyl substituted derivative, viz. trans-4,4Y-diheptyl-1,1X :4X ,1Y-tercyclohexylidene Ž6. w6x, shows that the structural features of the tercyclohexylidene bridge are satisfactorily reproduced at the RHFr6-31G level ŽTable 1.. As expected, the highest occupied MO’s of compounds 1–5 are p-like. The RHFr6-31G p MO energies of 1–5 together with the p MO energies of two ethene molecules possessing the same relative geometry as found in 1, 2, 4 and 5, respectively, are

3. Results and discussion 3.1. Ground state properties of compounds 1–5 In Fig. 1, the RHFr6-31G geometry of 1,1X-bicyclohexylidene Ž1. is shown. As discussed in our preliminary account w12x, the RHFr6-31G results

X

X

Y

Fig. 2. RHFr6-31G geometry of 1,1 :4 ,1 -tercyclohexylidene Ž2..

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

142

Table 1 ˚ ., valence angles Ž8. and dihedral angles Ž8. of 2. Between parentheses the single crystal X-ray data for Calculated bond lengths ŽA Y X X Y trans-4,4 diheptyl-1,1 :4 ,4 -tercyclohexylidene Ž6. is presenteda Bond length

˚. ŽA

Valence angles

Ž8.

Dihedral angles

Ž8.

CŽ1. –CŽ4.

1.55 Ž1.52. 1.52 Ž1.50. 1.34 Ž1.34. 1.52 Ž1.52. 1.54 Ž1.53. 1.53 Ž1.52.

CŽ1. –CŽ4. –CŽ5.

111.7 Ž112.3. 110.2 Ž110.1. 124.9 Ž125.7. 124.9 Ž124.1. 111.3 Ž112.3. 111.5 Ž112.2. 111.0 Ž109.3.

CŽ1. –CŽ6. –CŽ8. –CŽ10.

179.6

CŽ1. –CŽ6. –CŽ8. –CŽ12.

0.9

CŽ1. –CŽ6. CŽ5. –CŽ7. CŽ7. –CŽ9. CŽ9. –CŽ13. CŽ13. –CŽ17.

CŽ1. –CŽ6. –CŽ3. CŽ4. –CŽ5. –CŽ7. CŽ5. –CŽ7. –CŽ9. CŽ7. –CŽ9. –CŽ13. CŽ9. –CŽ13. –CŽ17. CŽ13. –CŽ17. –CŽ15.

a

For single crystal X-ray data of 6 see Ref. w6x.

given in Table 2. The lowest RHFr6-31G Koopmans w25x ionization potential ŽIP. of 1 ŽIP1 8.48 eV. is well separated from the next ionization potential IP2 Ž10.89 eV.; both values are in reasonable agreement with available photoelectron spectroscopy data Ž1: IP1 8.16 eV, IP2 9.8 eV. w5,26x. In the case of 2, 4 and 5, a splitting of ca. 0.6 eV between the HOMO and HOMO-1 is found, while for the ethene analogue both p MO energies remain nearly degenerate. This near degeneracy for the p MO energies of both ethene molecules in the geometry of 2 is also observed, if ghostcentres, with the appropriate basisfunctions, are placed on the positions of the missing

Table 2 p MO Energies of compounds 1, 2, 3, 4 and 5

Fig. 3. RHFr6-31G geometries of 1,4-diisopropylidene-cyclohexane Ž4. and 1,4-dimethylidene-cyclohexane Ž5.. Selected ˚ RHFr6-31G structural data of 4 and 5: 4 CŽ1. –CŽ4. 1.546 A, ˚ CŽ6. –CŽ8. 1.337 A, ˚ CŽ8. –CŽ10. 1.515 A, ˚ CŽ1. –CŽ6. 1.517 A, ˚ CŽ4. –CŽ1. –CŽ6. 111.678, CŽ1. –CŽ6. –CŽ8. CŽ5. –CŽ6. 2.976 A, ˚ 124.868, CŽ6. –CŽ8. –CŽ10. 124.668 and 5 CŽ1. –CŽ4. 1.545 A, ˚ CŽ6. –CŽ8. 1.326 A, ˚ CŽ5. –CŽ6. 2.908 A, ˚ CŽ1. –CŽ6. 1.512 A, CŽ4. –CŽ1. –CŽ6. 111.068, CŽ1. –CŽ6. –CŽ8. 122.998.

Compound

p MO energy ŽeV.

p MO energy a

1 2

y8.48 y8.85 y8.23 y8.62 y8.94 y8.30 y9.76 y9.07

y10.19 y10.09 y10.09 y10.19 y10.09 y10.09 y10.16 y10.15

3 4 5

a Energy of the p MO’s of two ethene molecules positioned in the same geometry Žsee text and Figs. 1–3.. For 2–5, the two ethene p MO energies are nearly degenerate.

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

atoms. Hence, this splitting can be attributed to through-bond interactions w16x involving interactions with MO’s centered on the cyclohexyl moieties. Unfortunately, no photoelectron spectroscopy data are available for 2 and 4. However, for 1,4-dimethylidene-cyclohexane Ž5., another reference compound, the experimental ionization potentials have been determined ŽIP1 9.0 eV, IP2 9.5 eV. w27x which are satisfactorily reproduced ŽRHFr6-31G Koopmans values; IP1 9.07 eV and IP2 9.76 eV.. 3.2. The lowest Õalence transitions of 1,1X-bicyclohexylidene (1) and tetramethylethene (3) For the assignment of the lowest valence transitions of compounds 1–4 the MRDCI method was used Žsee computational detail section.. In the case of 1 and 3, the four lowest states of each symmetry were calculated. In Table 3, the results are reported

143

for 1 and compared with those of our earlier ab initio MRDCI calculations w12x. On the basis of the calculated C 2h symmetry of 1, only the A u and B u excited states will have non-zero oscillator strengths Ž f .. Since the transition energies of the A u excited states are larger than 12 eV, while those of the B u excited states are in the range 9.40–12.39 eV, the latter were analyzed in detail with respect to the assignment of experimentally observable valence transitions. For the lowest two B u excited states the results of the calculations, in which, instead of ca. 5000 CSF’s per symmetry, ca. 60000 CSF’s were used, confirm the conclusions reached in our preliminary account w12x. The lowest symmetry allowed transition Ž9.47 eV, 1B u , f : 0.9401, HOMO™ LUMO. is assigned to a p ™ p ) transition, whereas the second lowest symmetry allowed transition Ž10.65 eV, 2B u , f : 0.1459, HOMO™ LUMOq 1. corresponds to a p ™ s ) transition. In line with experiment w8,9x, both transi-

Table 3 The four lowest state energies of each symmetry of 1, transition energies, oscillator strengths and polarizationa,b State symmetry

Energy ŽHartree.

Transition energy ŽeV.

Oscillator strength Ž f .

1A g

y466.01168043 Žy465.938378. y465.58105391 Žy465.410614. y465.57331302 y465.57124622 y465.56891635 Žy465.500749. y465.55297510 Žy465.488344. y465.51208008 y465.51026451 y465.66381639 Žy465.597163. y465.62034468 Žy465.552797. y465.58347980 y465.55634923 y465.62752955 Žy465.560505. y465.58496364 Žy465.518276. y465.54587853 y465.54487154

11.72 Ž14.36. 11.93 11.99 12.05 Ž11.91. 12.48 Ž12.25. 13.60 13.64 9.47 Ž9.28. 10.65 Ž10.49. 11.65 12.39 10.45 Ž10.28. 11.61 Ž11.43. 12.68 12.70

0.0000 Ž0.0000. 0.0000 0.0000 0.1139 Ž0.1126. 0.0140 Ž0.0086. 0.0401 0.0005 0.9401 Ž0.8494. 0.1459 Ž0.1282. 0.1361 0.0513 0.0000 Ž0.0000. 0.0000 Ž0.0000. 0.0000 0.0000

2A g 3A g 4A g 1A u 2A u 3A u 4A u 1B u 2B u 3B u 4B u 1B g 2B g 3B g 4B g a

Polarizationa

H H H H 5 5 HH 5

Notation; 5: polarized parallel to the double bond; H : polarized perpendicular to the double bond in plane with the carbon atoms CŽ3. to CŽ6.; HH : polarized perpendicular to the double bond and perpendicular to the plane occupied by the carbon atoms CŽ3. to CŽ6. Žsee Fig. 1.. b Numbers between parentheses are taken from the preliminary account w12x.

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

144

Table 4 Mulliken population analysis w13x of the ground state and Mulliken population differences for the excited states of 1 Atom

CŽ1.,CŽ2. CŽ3.,CŽ4.,CŽ5., CŽ6. CŽ7.,CŽ8.,CŽ9., CŽ10. CŽ11.,CŽ12. HŽ13.,1HŽ14., HŽ15.,HŽ16. HŽ17.,HŽ18., HŽ19.,HŽ20. HŽ21.,HŽ22., HŽ23.,HŽ24. HŽ25.,HŽ26., HŽ27.,HŽ28. HŽ29.,HŽ30. HŽ31.,HŽ32.

State 1A g

1A u a

2A u a

3A u a

4A u a

1B u a

2B u a

3B u a

4B u a

1B g a

5.993 6.337

y0.249 0.051

0.139 y0.030

y0.021 y0.079

y0.047 y0.034

y0.062 y0.004

y0.208 y0.021

y0.218 y0.005

y0.208 0.007

0.170 y0.073

6.293

y0.089

y0.040

y0.030

y0.068

y0.024

y0.023

y0.027

y0.031

y0.005

6.301 0.843

0.048 0.025

y0.086 0.041

y0.051 0.110

y0.055 0.006

y0.019 0.024

0.014 y0.018

y0.010 0.090

y0.068 y0.026

y0.031 0.029

0.835

y0.004

y0.019

y0.020

y0.018

0.007

0.147

y0.005

0.035

y0.016

0.848

0.063

0.000

0.003

0.113

0.008

0.014

0.060

0.031

y0.004

0.847

0.066

0.003

0.005

0.000

0.023

y0.009

y0.011

0.016

y0.005

0.854 0.847

y0.008 y0.015

0.028 0.005

0.092 y0.001

0.006 0.096

0.017 y0.005

y0.004 0.019

0.024 0.000

0.095 0.107

0.011 y0.002

a

For the excited states a positive number indicates an increase in electron population, while a negative number corresponds to a decrease in electron population.

Table 5 The four lowest state energies of each symmetry of 3, transition energies, oscillator strengths and polarizationa,b State symmetry

Energy ŽHartree.

Transition energy ŽeV.

oscillator strength Ž f .

1A 1

y234.45531014 Žy234.086330. y234.00214566 Žy233.701057. y233.97936270 y233.93549268 y234.09295710 Žy233.867100. y234.04609206 Žy233.818473. y233.98643967 y233.93990486 y234.09854990 Žy233.882086. y234.06300208 Žy233.838799. y234.03810094 y233.97296995 y234.06052501 Žy233.833501. y234.01000115 Žy233.787136. y233.94780288 y233.93834612

12.33 Ž14.68. 12.95 14.15 9.86 Ž10.16. 11.14 Ž11.48. 12.76 14.03 9.71 Ž9.75. 10.68 Ž10.93. 11.35 13.13 10.74 Ž11.07. 12.12 Ž12.34. 13.81 14.07

0.0000

2A 1 3A 1 4A 1 1B1 2B1 3B1 4B1 1B 2 2B 2 3B 2 4B 2 1B 3 2B 3 3B 3 4B 3

Polarizationa

0.0000 0.0000 0.0337

HH

0.0447

HH

0.0002 0.0030 1.0870

HH HH 5

0.0042

5

0.0000 0.0102 0.0011

5 5 H

0.0002

H

0.0178 0.1259

H H

a Notation; 5: polarized parallel to the double bond; H : polarized perpendicular to the double bond in plane with the carbon atoms CŽ3. to CŽ6.; HH : polarized perpendicular to the double bond and perpendicular to the plane occupied by the carbon atoms CŽ3. to CŽ6.. b Numbers between parentheses are taken from the preliminary account w12x.

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

tions are polarized along the carbon–carbon double bond CŽ1. –CŽ2. ŽTable 3.. The changes in electron population ŽMulliken population analysis w13x. upon excitation from the 1A g ground state to the 1B u and 2B u excited state, respectively, suggest that the 2B u excited state possesses charge transfer character. Electron density shifts from the carbon–carbon double bond CŽ1. –CŽ2. towards the equatorial hydrogen atoms of the cyclohexylidene rings ŽTable 4.. The first symmetry forbidden s ™ p ) transition is the 1A g ™ 1B g transition Ž10.45 eV, f : 0.0000, HOMO-1™ LUMO. possesses a lower excitation energy than the first p ™ s ) transition Ž10.65 eV, 1A g ™ 2B u , f 0.1459, HOMO™ LUMOq 1.. The electron redistribution upon excitation to the 1B g excited state indicates that electron density shifts from the cyclohexylidene ring moieties, viz. the allylic carbon atoms CŽ3. to CŽ6., towards the olefinic carbon atoms CŽ1. and CŽ2. ŽFig. 1 and Table 4.. To assess the effect of the presence of the cyclohexane-like moieties on the MRDCI results in the case of 1, transition energies as well as oscillator strengths for the four lowest valence transitions of each symmetry were calculated for the reference compound tetramethylethene Ž3. using a similar approach ŽTable 5.. The first excited state of 3 has to be assigned to a p ™ p ) excitation Ž9.71 eV, 1B 2 , f : 1.0870, HOMO™ LUMO; experimental 7.0 eV w7x.. The second excited state is a p ™ s ) excitation Ž9.86 eV, 1B1 , f : 0.0337, HOMO™ LUMOq 1., whereas the third excited state corresponds to a s ™ p ) excitation Ž10.68 eV, 2B 2 , f : 0.0042, HOMO-1™ LUMO.. Again these assignments are in line with our earlier MRDCI results in which, instead of ca. 88000 CSF’s per symmetry, only ca. 8500 CSF’s were used w12x.

145

A comparison of the calculated valence transitions of 1 and 3 shows that the second ŽHOMO™ LUMO q 1. and third ŽHOMO-1™ LUMO. transitions of 3 are interchanged with the second ŽHOMO-1™ LUMO. and third ŽHOMO™ LUMOq 1. transitions of 1. Presumably, this is a consequence of the lower second ionization potential ŽIP2 . of 1. Whereas for 3 IP1 and IP2 equal 8.62 eV and 12.07 eV, in the case of 1 the corresponding values are 8.48 eV and 10.89 eV, respectively. Hence, IP2 of 1 is lowered by 1.18 eV, and, therefore, the second and third valence transitions of 1 are interchanged compared to those of 3. 3.3. Direct-CI calculations on the lowest Õalence excited states of 1,1X-bicyclohexylidene (1) To assess the reliability of the MRDCI approach for the calculation of the valence transitions of 1, i.e. in particular the applied frozen core approximation as well as the configuration selection procedure w14,15,20x, Direct-CI w17x calculations were performed on the 1A g ground state Ž6015806 states., the 1B u Ž p ™ p ) , HOMO™ LUMO. Ž18135443 states., 2B u Ž p ™ s ) , HOMO ™ LUMO q 1. Ž18135443 states. and 1B g Ž s ™ p ) , HOMO-1™ LUMO. Ž21633690 states. excited states ŽTable 6.. In these calculations only the MO’s corresponding to the carbon 1s atomic orbitals were frozen. In general, the MRDCI excitation energies of the lowest transitions deviate ca. 1.2 eV from the Direct-CI values. The error of 2.3 eV for the lowest p ™ p ) transition energy calculated by the Direct-CI method Ž8.29 eV., compared to experiment Ž p ™ p ) 6.01 eV w5,6x., is attributed to the use of the relatively small 6-31G basis set.

Table 6 A comparison of excitation energies of 1 calculated by the Direct-CI method and the MRDCI method State symmetry

Energy ŽDirect-CI in Hartree.

Transition energy ŽDirect-CI in eV.

Transition energy ŽMRDCI in eV.

1A g 1B u 2B u 1B g

y466.9492014043a y466.6444857635 y466.5983986031 y466.6133027111

8.29 9.55 9.14

9.47 10.65 10.45

a

MRDCI ground state energy: y466.01168043 Hartree.

146

Table 7 Comparison of c 2 in the CI vector calculated by the MRDCI method and the Direct-CI method for compound 1. Only c 2 ) 0.0001 are tabulated 1A g state MO Direct

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Y

0.93004 0.00646

0.77845 0.00616 0.00019 0.00053 0.00011 0.00015 0.00035 0.00025 0.00011

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 1 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 – – – 1 – – – –

– 2 – 1 2 1 1 1 1

– – 2 1 – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – 1 – – –

– – – – – – – – –

– – – – – – 1 – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – – –

– – – – – – – 1a 1b

0.00257

Y is an unoccupied MO: a Ys 72 and b Ys84. 1B u state MO MRDCI

Direct

0.92397 0.00008

0.77631 0.00179 0.00061 0.00070 0.00012 0.00013 0.00011 0.00016

X

36

37

38

39

40

41

42

43

44

– 2 2 2 2 2 2 2 2 2 – 2 2 2 2 2 2 2 2 2 – 2 2 2 2 2 2 2 2 1 – 2 2 2 2 2 2 2 2 2 – 1 2 2 2 2 2 2 2 2 – 2 2 2 2 2 2 2 2 2 1a 2 2 2 2 2 2 2 2 2 1c 2 2 2 2 2 2 2 2 2 0.00019 – 2 2 2 2 2 2 2 2 2 0.00512 – 2 2 2 2 2 2 2 2 2 X is an occupied MO and Y is an unoccupied MO: a X s19, b Ys 70 and c X s 35.

45

46

47

48

49

50

51

52

53

54

55

56

57

Y

2 2 2 1 2 2 2 2 2 2

1 1 2 2 2 1 2 2 1 1

1 – – – – – – – – –

– 1 – – – – – – – –

– – 1 – – – – – – –

– – – – – – – – – -

– – – 1 1 – – – – –

– – – – – – – – 1 –

– – – – – – – – – –

– – – – – 1 – – – 1

– – – – – – – – – –

– – – – – – – – – –

– – – – – – – – – –

– – – – – – 1b 1b – –

2B u state MO MRDCI

Direct

X

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

Y

0.00077 0.87488

0.00170 0.77401 0.00120 0.00036 0.00024

– – – – 1a

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

2 2 2 2 2

2 2 1 2 2

2 2 2 1 2

1 l 2 2 1

1 – – – 1

– 1 – – 1

– – 1 – –

– – – – –

– – – 1 –

– – – – –

– – – – –

– – – – –

– – – – –

– – – – –

– – – – –

– – – – –

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

MRDCI

0.03162

0.01414

1b – – – – – – 1f 1h 1i – – – – –

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 1 2 2 2

2 1 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 1 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 1 2 2 2 2 2 1 1 2

1 l 0 1 1 – 1 1 1 1 1 1 1 1 1

1 1 1 – – – – – – – – – – – –

1 1 – – – 1 – 1 1 1 1 1 1 1 –

– – 1 – – – – – – – – – – – –

– – – – – – – – – – – – – – –

– – – – – – 1 – – – – – – – –

– – – – – – – – – – – – – – 1

– – – – – – – – – – – – – – –

– – – 1 – – – – – – – – – – –

– – – – – – – – – – – – – – –

– – – – – – – – – – – – – – –

– – – – – – – – – – – – – – –

– – – – 1c 1d 1e 1g 1g 1j 1g 1k 1k 1l –

X is an occupied MO and Y is an unoccupied MO: a X 31, b X s 35, c Ys126, d Ys84, e Ys 73, f X s 28, g Ys 72, h X s 33, i X s 34, j Ys60, k Ys 79 and l Ys103. 1B g state MO MRDCI

Direct

X

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

Y

0.84382 0.04809

0.73092 0.03760 0.00697 0.00091 0.00027 0.00039 0.00020 0.00025 0.00023 0.00039 0.00015 0.00040 0.00020 0.00012

– – – – 1b – – – 1c – – – – – – – –

2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

1 1 2 2 2 2 2 2 2 2 1 1 1 1 2 2 2

2 2 2 2 2 2 2 2 1 1 2 2 2 2 1 1 1

1 – – – 1 1 1 1 2 2 – – – – – – –

– 1 – – – – – – – – – – – – – – –

– – 1 – – – – – – – – – – – – – –

– – – – – – – – – – – – – – – – –

– – – – – – – – – – – – – – 1 – –

– – – – – – – – – – 1 – – – – – –

– – – – – – – – – – – – – – – – –

– – – – – – – – – – – 1 – – – – –

– – – – – – – – – – – – – – – – –

– – – – – – – – – – – – – – – – –

– – – – – – – – – – – – – – – 1 –

– – – 1a – – – – – – – – 1d 1e – – 1f

0.00546 0.00925 0.00410 0.00475 0.00949 0.00212 0.00047 0.00033 0.00180

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

0.00016 0.00011 0.00020 0.00025 0.00012 0.00014 0.00013 0.00013 0.00026 0.00010 0.00018 0.00011 0.00016 0.00013

X is an occupied MO and Y is an unoccupied MO: a Ys 59, b X s 21, c X s 33, d Ys 76, e Ys90 and f Y s60.

147

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

148

Table 8 The four lowest state energies of each symmetry of 2, transition energies, oscillator strengths and polarizationa State symmetry

Energy ŽHartree.

Transition energy ŽeV.

Oscillator strength Ž f .

1A g 2A g 3A g 4A g 1A u 2A u 3A u 4A u 1B u 2B u 3B u 4B u 1B g 2B g 3B g 4B g

y697.73959400 y697.39433023 y697.37881228 y697.35031251 y697.36336514 y697.31898405 y697.29482069 y697.29209258 y697.40045266 y697.36908646 y697.34007607 y697.31483176 y697.35336642 y697.30381066 y697.29289548 y697.28367959

9.40 9.82 10.59 10.24 11.45 12.10 12.18 9.23 10.08 10.87 11.56 10.51 11.86 12.16 12.41

0.0000 0.0000 0.0000 0.0004 - 0.0001 0.0067 0.1832 1.8993 0.1956 0.1340 0.1895 0.0000 0.0000 0.0000 0.0000

Polarizationa

H H H H 5 Ž188 HH. 5 Ž248 HH. 5 Ž148 HH. HH Ž78 5.

a

Notation; 5: polarized parallel to the double bond; H : polarized perpendicular to the double bond in plane with the carbon atoms CŽ1., CŽ3., CŽ10. and CŽ11., CŽ2., CŽ4., CŽ9., CŽ12.; HH : polarized perpendicular to the double bond and perpendicular to the planes occupied by the carbon atoms CŽ1., CŽ3., CŽ10., CŽ11. and CŽ2., CŽ4., CŽ9., CŽ12., respectively Žsee Fig. 2.. Between parentheses the angle Ž8. with the specified polarization direction is denoted.

In spite of the difference in transition energy of more than 1 eV, the most important configurations in the CI vector calculated by both the MRDCI and the

Direct-CI method for each state are essentially identical ŽTable 7.. Thus, the MRDCI frozen core approximation and configuration selection procedure

Table 9 Mulliken population analysis w13x of the ground state and Mulliken population differences of the excited states of 2 Atom

CŽ1., CŽ2., CŽ3., CŽ4. CŽ5., CŽ6. CŽ7., CŽ8. CŽ9., CŽ10., CŽ11., CŽ12. CŽ13., CŽ14., CŽ15., CŽ16. CŽ17., CŽ18. HŽ19., HŽ20., HŽ21., HŽ22. HŽ23., HŽ24., HŽ25., HŽ26. HŽ27., RŽ28., HŽ29., HŽ30. HŽ31., HŽ32. HŽ33., HŽ34., HŽ35., HŽ36. HŽ37., HŽ38., HŽ39., HŽ40. HŽ41., HŽ42., HŽ43., HŽ44. HŽ45., HŽ46. a

State 1A g

4A u a

1B u a

1B u a

3B u a

4B u a

1A u a

1B g a

6.329 6.001 5.999 6.336 6.293 6.305 0.836 0.843 0.847 0.854 0.834 0.834 0.847 0.845

0.000 y0.124 y0.137 y0.005 y0.032 0.014 0.004 0.032 0.039 y0.003 0.032 0.035 0.022 y0.005

0.001 y0.013 y0.016 y0.002 y0.005 y0.010 y0.005 0.008 0.002 0.008 0.004 0.001 0.011 y0.002

y0.019 y0.083 y0.064 y0.010 y0.008 y0.009 0.038 0.011 0.005 0.006 0.030 0.018 0.007 0.002

y0.015 y0.078 y0.135 y0.024 y0.021 y0.011 y0.005 0.014 0.026 0.019 0.020 0.073 0.018 0.032

y0.024 y0.147 y0.119 0.000 y0.005 y0.004 0.174 0.004 0.001 y0.001 y0.004 y0.005 y0.006 y0.002

y0.037 0.083 0.098 y0.038 y0.006 y0.019 0.008 0.013 y0.001 0.005 y0.014 y0.008 y0.002 y0.001

y0.044 0.079 0.084 y0.040 y0.010 y0.021 0.020 0.017 0.000 0.006 y0.005 y0.008 y0.004 y0.001

For the excited states a positive number indicates an increase in electron population, while a negative number corresponds to a decrease in electron population.

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

can be applied for the study of the optical properties of the oligoŽcyclohexylidenes.. These results provide additional support for the reliability of the assignment of the lowest valence excited states of 1. 3.4. The lowest Õalence transitions of 1,1X :4X ,1Ytercyclohexylidene (2) and 1,4-diisopropylidenecyclohexane (4) The MRDCI transition energies, oscillator strengths Ž f . and polarization of the four lowest states of each symmetry for 2 are reported in Table 8. A survey of the data reveals that the 1B u and 2B u states correspond to the two p ™ p ) ŽHOMO™ LUMO and HOMO-1 ™ LUMO q 1. transitions, which are both polarized along the double bonds CŽ5. –CŽ7. and CŽ6. –CŽ8.. As expected, Mulliken population analysis w13x shows that for these excited states no significant electron redistribution occurs ŽTable 9.. The excitation to the 3B u state Ž10.87 eV, f : 0.1304. corresponds to a p ™ s ) transition, which despite its multi-reference character possesses mainly HOMO ™ LUMO q 2 character Žc 2 HOMO ™ LUMOq 2: 0.65; HOMO-1™ LUMOq 3: 0.12.. In analogy with the 2B u excited state of 1, it is polar-

149

ized along the carbon–carbon double bonds CŽ5. – CŽ7. and CŽ6. –CŽ8.. Among the A u states, only the 4A u excitation does not have a vanishingly low oscillator strength. The other A u excited states Ž1A u , 2A u and 3A u . wil not be analyzed further. The 4A u Ž12.18 eV, f : 0.1832, HOMO-1™ LUMOq 8. excited state resembles the 1A u state of 1 and is assigned to a p ™ s ) transition, which is polarized perpendicular to the carbon–carbon double bonds CŽ5. –CŽ7. and CŽ6. –CŽ8., and, in plane of the carbon atoms CŽ1., CŽ3. and CŽ10.. The 4B u excited state Ž11.56 eV, f : 0.1895, HOMO™ LUMOq 9. of 2 and the 3B u excited state of 1 are both p ™ s ) transitions, polarized perpendicular to both the carbon–carbon double bonds ŽCŽ5. –CŽ7. and CŽ6. –CŽ8.. as well as perpendicular to the plane of carbon atoms ŽCŽ1., CŽ3. and CŽ10... As shown by Mulliken population analyses w13x, the p ™ s ) transitions again possess charge transfer character; electron density shifts from the carbon–carbon double bonds towards the cyclohexylidene rings. Upon excitation to the 3B u state, the electron population on CŽ7. and CŽ8. decreases, while that on the equatorial hydrogen atoms HŽ37. to HŽ40. present in the outermost cyclohexylidene

Table 10 The four lowest state energies of each symmetry of 4, transition energies, oscillator strengths and polarizationa State symmetry

Energy ŽHartree.

Transition energy ŽeV.

Oscillator strength Ž f .

1A g 2A g 3A g 4A g 1A u 2A u 3A u 4A u 1B u 2B u 3B u 4B u 1B g 2B g 3B g 4B g

y466.07398855 y465.70906496 y465.67695235 y465.62742550 y465.64414321 y465.61766446 y465.57797425 y465.52268976 y465.71266676 y465.66657187 y465.62941731 y465.58818592 y465.64013896 y465.58117264 y465.55988660 y465.53251783

9.93 10.80 12.15 11.70 12.42 13.50 15.00 9.83 11.09 12.10 13.22 11.81 13.41 13.99 14.73

0.0000 0.0000 0.0000 0.0002 0.0590 0.0005 0.0239 1.6150 0.7306 0.0855 0.0397 0.0000 0.0000 0.0000 0.0000

a

Polarizationa

H H H H 5 5 5 Ž428 HH. 5 Ž98 HH.

Notation; 5: polarized parallel to the double bond; H : polarized perpendicular to the double bond in plane with the carbon atoms CŽ1., CŽ3., CŽ10. and CŽ11., CŽ2., CŽ4., CŽ9., CŽ12.; HH : polarized perpendicular to the double bond and perpendicular to the planes occupied by the carbon atoms CŽ1., CŽ3., CŽ10., CŽ11. and CŽ2., CŽ4., CŽ9., CŽ12., respectively Žsee Fig. 3.. Between parentheses the angle Ž8. with the specified polarization direction is denoted.

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

150

rings increases. For the 4A u excited state, the electron population of the olefinic carbon atoms CŽ5. to CŽ8. decreases, whereas concomitantly that on the equatorial hydrogen atoms HŽ37. to HŽ40. and axial hydrogen atoms HŽ23. to HŽ30. of the outermost cyclohexylidene rings as well as the equatorial hydrogen atoms HŽ33. to HŽ36. of the central cyclohexylidene ring increases. In the 4B u excited state, the electron population on the olefinic carbon atoms CŽ5. to CŽ8. decreases while the electron population of the axial hydrogen atoms HŽ19. to HŽ22. of the central cyclohexylidene ring increases. The 2A g and 3A g excited states correspond to the symmetry forbidden p ™ p ) transitions HOMO™ LUMOq 1 and HOMO-1™ LUMO, respectively. The 1A g ™ 1A u Ž s ™ p ) , 10.24 eV, f : 0.0004, HOMO-2™ LUMO. transition, which possesses only a small oscillator strength, is polarized perpendicular to the double bonds ŽCŽ5. –CŽ7. and CŽ6. –CŽ8.., but in plane of the carbon atoms ŽCŽ1., CŽ3. and CŽ10... The excitation to the 1B g state Ž10.51 eV, f : 0.0000, HOMO-2™ LUMOq 1., which is symmetry forbidden, of 2 corresponds to a s ™ p ) transition. Upon excitation to either the 1A u or 1B g excited states of 2 the electron population on CŽ1. to CŽ4. and CŽ9. to CŽ12. decreases, while that on the olefinic carbon atoms increases ŽTable 9.. Compared to 1 the lowest lying active s ™ p ) excitation is lowered in energy Ž1; 1A u ; 12.05 eV and 2; 1A u ; 10.24 eV., but the oscillator strength Ž f . also decreases Ž1; f : 0.1139 and 2; f : 0.0004.. To further corroborate the assignment of the low-

est valence transitions of 2 and the effect of the outermost cyclohexane-like rings on the calculated valence transitions, the reference compound 1,4-diisopropylidene-cyclohexane Ž4. was also studied using the ab initio MRDCI method ŽTable 10.. Again the excitations to the 1B u and 2B u states have to be assigned to p ™ p ) transitions Ž9.83 eV and 11.09 eV; f : 1.6150 and 0.7306; HOMO™ LUMO and HOMO-1™ LUMOq 1, respectively.. The charge redistribution upon excitation to the A u and B u states is presented in Table 11. It is noteworthy that the transition energies for 4 are all hypsochromically shifted by ca. 0.7 eV with respect to those of 2, presumably due to the higher ionization potentials of 4. The RHFr6-31G Koopmans w25x ionization potentials of the p-MO’s of 2 are 8.23 eV and 8.86 eV, whereas for 4 the corresponding values are 8.30 eV and 8.94 eV, respectively, which are in satisfactory agreement. The next two lower ionization potentials of 2 are 10.75 eV and 11.33 eV, respectively, while for 4 they are 11.15 eV and 12.19 eV. All oscillator strengths, with the exception of those for the 2B u and 2A u state, increase in going from 4 to 2. This hypochromic effect can be rationalized by considering the increase in size of 2. The excitation to the 3B u state is assigned to a p ™ s ) excitation Ž12.10 eV; f : 0.0855; HOMO-1™ LUMO q 2., which has the largest coefficient in the CI vector Žc 2 : HOMO-1™ LUMOq 2: 0.47; HOMO ™ LUMOq 3: 0.38.. The electron redistribution upon excitation to the 3B u excited state indicates that the electron population on the carbon–carbon double

Table 11 Mulliken population analysis w13x of the ground state and Mulliken population differences of the excited states of 4 Atom

CŽ1., CŽ2., CŽ3., CŽ4. CŽ5., CŽ6. CŽ7., CŽ8. CŽ9., CŽ10., CŽ11., CŽ12. HŽ13., HŽ14., HŽ15., HŽ16. HŽ17., HŽ18., HŽ19., HŽ20. HŽ21., HŽ22., HŽ23., HŽ24. HŽ25., HŽ26., HŽ27., HŽ28. HŽ29., HŽ30., HŽ31., HŽ32. a

State 1A g

1A u a

2A u a

3A u a

4A u a

1B u a

2B u a

3B u a

4B u a

6.330 5.977 6.018 6.474 0.842 0.836 0.842 0.838 0.840

y0.039 0.069 0.096 y0.039 0.015 y0.001 0.007 y0.025 0.000

y0.056 y0.073 y0.121 y0.011 0.004 0.036 y0.013 0.099 0.039

y0.049 0.039 0.064 y0.046 0.005 0.018 0.013 0.009 0.001

y0.049 y0.011 y0.030 y0.083 0.070 y0.017 0.020 0.034 0.037

0.002 y0.001 y0.007 y0.004 0.013 y0.013 y0.003 0.005 0.003

y0.027 y0.055 y0.045 y0.011 y0.009 0.043 0.019 0.026 0.009

y0.003 y0.050 y0.100 y0.045 0.071 y0.017 0.044 y0.007 0.037

y0.014 y0.065 y0.126 y0.046 0.053 y0.015 0.047 0.025 0.045

For the excited states a positive number indicates an increase in electron population, while a negative number corresponds to a decrease in electron population.

R.W.A. HaÕenith et al.r Chemical Physics 225 (1997) 139–152

bonds decreases while that on the hydrogen atoms HŽ13. to HŽ16. and HŽ21. to HŽ24. increases ŽFig. 3, Table 11.. For 4, excitation to the 4B u state Ž p ™ s ) ; 13.22 eV; f : 0.0397. leads to an increase of the electron population on the outermost methyl groups, while it concomitantly decreases on the olefinic carbon atoms ŽCŽ5. to CŽ8... This transition also possesses multi-reference character Žc 2 : HOMO ™ LUMOq 3: 0.45; HOMO-1™ LUMOq 2: 0.38.. The 1A u excited state is assigned to a s ™ p ) transition Ž11.70 eV; f : 0.0002; HOMO-2 ™ LUMO.. The 2A u state is assigned to a p ™ s ) transition Ž12.42 eV; f : 0.0590; HOMO™ LUMOq 5.; upon excitation the electron population at the olefinic carbon atoms decreases, and that at the equatorial hydrogen atoms HŽ25. to HŽ28. of the cyclohexane ring increases. Thus from a comparison of the results obtained for 2 and 4, it can be concluded, that the outermost cyclohexylidene rings in 2 do have an influence on the lowest lying p ™ s ) transitions; oscillator strengths in the case of 2 increase compared to that of 4 Ž1A g ™ 1B u ; 2, f : 1.8993 and 4, f : 1.6150.. In summary, the 1B u and 2B u state of 2 and 4 are p ™ p ) transitions. However, the excitation energies for 4 are larger Ž2: 9.23 eV, 10.08 eV and 4: 9.83 eV, 11.09 eV.. The 3B u state of 2 Ž p ™ s ) transition. corresponds to the 3B u state of 4, but it possesses considerably less multi-reference character. Moreover, the excitation energy to the 3B u state of 2 is lower than that for 4 Ž2: 10.87 eV and 4: 12.10 eV.. Notwithstanding, the electron redistribution upon excitation to the 3B u state has the same characteristics, i.e. a decrease in electron population on the olefinic carbon atoms concomitant with an increase in electron population on the hydrogen atoms is found. In the case of 2 and 4, hydrogen atoms positioned in the outermost cyclohexylidene rings and the methyl groups, respectively, are involved.

4. Conclusions The lowest valence transitions for the oligoŽcyclohexylidenes., 1,1X-bicyclohexylidene Ž1. and 1,1X ;4X ,1Y-tercyclohexylidene Ž2. were assigned using ab initio MRDCI calculations. In the case of 1, the MRDCI results were verified using Direct-CI

151

calculations; the most important configurations in the CI vector were identical for each state. For 1 three valence transitions were found possessing p ™ p ) Ž1B u ; 9.47 eV, f : 0.9401., s ™ p ) Ž1B g ; 10.45 eV, f : 0.0000. and p ™ s ) Ž2B u ; 10.65 eV, f : 0.1459. character, respectively. In line with experiment, the p ™ p ) and p ™ s ) transitions are polarized along the carbon–carbon double bond CŽ1. –CŽ2.. A comparison with the results calculated for tetramethylethene Ž3; p ™ p ) Ž1B 2 ; 9.71 eV, f : 1.0870., p ™ s ) Ž1B1; 9.86 eV, f : 0.0337. and s ™ p ) Ž2B 2 ; 10.68 eV, f : 0.0042., respectively. shows that for 1 the second transition has to be assigned to a s ™ p ) transition, whereas for 3 the second transition corresponds to a p ™ s ) transition. This is a consequence of the lower second ionization potential of 1 ŽIP2 10.89 eV. with respect to that of 3 ŽIP2 12.07 eV.. In the case of 2, two active p ™ p ) transitions Ž1B u ; 9.23 eV, f : 1.8993 and 2B u ; 10.08 eV, f : 0.1956. and three active p ™ s ) transition Ž3B u ; 10.87 eV, f : 0.1340, 4B u ; 11.56 eV, f : 0.1895 and 4A u ; 12.18 eV, f : 0.1832.. In addition, a p ™ s ) Ž2A u ; 11.45 eV, f : - 0.0001. and two s ™ p ) Ž1A u ; 10.24 eV, f : 0.0004 and 3A u ; 12.10 eV, f : 0.0067. transitions are found which possesses very low oscillator strengths. For 1,4-diisopropylidenecyclohexane Ž4. the corresponding transitions are hypsochromically shifted. According to Mulliken population analyses the p ™ s ) transitions of oligoŽcyclohexylidenes. 1–2 possess charge transfer character; upon excitation electron density shifts from the olefinic carbon atoms towards equatorial hydrogen atoms of the cyclohexylidene rings. Acknowledgements Financial support from NCF and Cray Research Inc for R.W.A. Havenith ŽNCF grant CRG 96.18. is gratefully acknowledged. References w1x F.J. Hoogesteger, J.M. Kroon, L.W. Jenneskens, E.J.R. Sudholter, T.J.M. de Bruin, J.W. Zwikker, E. ten Grotenhuis, ¨ C.H.M. Maree, ´ N. Veldman, A.L. Spek, Langmuir 12 Ž1996. 4760.

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